Finite Group Databasebeta

← #7078122

Subgroups — #7078122

Order 512.

1571 conjugacy classes of subgroups.

The subgroup lattice has 1297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59271C211yesmaximal, characteristic, complemented
2#59224C211yesmaximal, characteristic
3#32540C211yesmaximal, characteristic, complemented
4#32538C211yesmaximal, characteristic, complemented
5#32436C211yesmaximal, characteristic, complemented
6#32435C211yesmaximal, characteristic, complemented
7#32073C211yesmaximal, characteristic, complemented
8#32069C211yesmaximal, characteristic, complemented
9#30671C211yesmaximal, characteristic, complemented
10#30664C211yesmaximal, characteristic, complemented
11#28776C211yesmaximal, characteristic, complemented
12#27589C211yesmaximal, characteristic, complemented
13#27585C211yesmaximal, characteristic, complemented
14#27496C211yesmaximal, characteristic, complemented
15#27488C211yesmaximal, characteristic, complemented
16#26572C211yesmaximal, characteristic, complemented
17#26568C211yesmaximal, characteristic, complemented
18#25955C211yesmaximal, characteristic, complemented
19#25952C211yesmaximal, characteristic, complemented
20#25211C211yesmaximal, characteristic, complemented
21#25203C211yesmaximal, characteristic, complemented
22#24875C211yesmaximal, characteristic, complemented
23#24873C211yesmaximal, characteristic
24#24695C211yesmaximal, characteristic, complemented
25#24690C211yesmaximal, characteristic, complemented
26#24264C211yesmaximal, characteristic
27C2×#2055C211yesmaximal, characteristic, complemented
28#22706C211yesmaximal, characteristic, complemented
29#22437C211yesmaximal, characteristic, complemented
30#22065C211yesmaximal, characteristic, complemented
31#21962C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#485C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic
35C2×#475C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2762—21no—
46#2756—21no—
47#2754—21no—
48#2737—21no—
49#2610—21no—
50#2569—21no—
51#2565C2211yescharacteristic, complemented
52#2563C2211yescharacteristic
53#2561—21no—
54#2532—21no—
55#2531—21no—
56#2520—21no—
57#2514C2211yescharacteristic, complemented
58#2513C2211yescharacteristic
59#2513C2211yescharacteristic
60#2511C2211yescharacteristic, complemented
61#2510—21no—
62#2500C2211yescharacteristic
63#2499C2211yescharacteristic, complemented
64#2498—21no—
65#2491C2211yescharacteristic
66#2489C2211yescharacteristic, complemented
67#2472—21no—
68#2442C2211yescharacteristic
69#2440C2211yescharacteristic
70#2423C2211yescharacteristic, complemented
71#2420C2211yescharacteristic
72#2412—21no—
73#2409C2211yescharacteristic
74#2408C2211yescharacteristic
75#2363C2211yescharacteristic
76#2362C2211yescharacteristic, complemented
77#2356C2211yescharacteristic, complemented
78#2354C2211yescharacteristic
79#2352C2211yescharacteristic
80#2352C2211yescharacteristic
81#2343—21no—
82#2342—21no—
83Q8×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85C4×#123C2211yescharacteristic
86C2×#391C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2285C2211yescharacteristic
89#2283C2211yescharacteristic
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2036C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2025C2211yescharacteristic
127#2024C2211yescharacteristic, complemented
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1992C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1948C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1940C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic, complemented
163#1924C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1875C2211yescharacteristic
171#1873C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1850C2211yescharacteristic, complemented
186#1835C2211yescharacteristic, complemented
187#1817C2211yescharacteristic
188#1808C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic, complemented
193#1804C2211yescharacteristic
194#1803C2211yescharacteristic, complemented
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#106C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201#1735C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#123D411yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120—21no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117—21no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C42C2311yescharacteristic
240#485—42no—
241#482—42no—
242#478—42no—
243#475—42no—
244#465—42no—
245#465—42no—
246#440—42no—
247#440—42no—
248C8×D4—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8—24no—
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102—42no—
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#401—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#393—21no—
335#393—21no—
336#393—21no—
337#393—21no—
338#392—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388D411yescharacteristic
383#388D411yescharacteristic
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386D411yescharacteristic
407#385—21no—
408#385—21no—
409#385—21no—
410#385D411yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#383—21no—
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381—21no—
425#381—21no—
426#381D411yescharacteristic
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#376—21no—
460#376—21no—
461C2×#95—21no—
462C2×#95—21no—
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—416no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8#4114yes—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557#125—41no—
558#125—41no—
559#124—82no—
560#123—42no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—82no—
566#121—22no—
567#121—41no—
568#121—41no—
569#121—41no—
570#120—82no—
571C4×Q8—22no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581#117—44no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—82no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—44no—
658C2×C22⋊C4—82no—
659C2×C22⋊C4—82no—
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C42—22no—
669C2×C42—22no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—41no—
740#97—41no—
741C4×C8—22no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—42no—
817C2×Q8—44no—
818C2×Q8—44no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—82no—
825C2×Q8—82no—
826C2×Q8H(5,𝔽2)12yes—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4H(5,𝔽2)12yes—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C2×#4112yes—
913C22×C42−1+412yes—
914C22×C4C2511yescharacteristic
915SD16—28no—
916SD16—44no—
917SD16—44no—
918SD16—44no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—44no—
942C2×C8—82no—
943C2×C8—82no—
944C2×C8C2×#4112yes—
945C2×C8C2×#4112yes—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C42—22no—
1033C42—22no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—42no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—84no—
1080C23—84no—
1081C23—84no—
1082C23—84no—
1083C23—162no—
1084C23—162no—
1085C23—162no—
1086C23#54712yes—
1087C23#57512yes—
1088C23#57712yes—
1089C23C23×D411yescharacteristic
1090Q8—22no—
1091Q8—22no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—84no—
1099Q8—162no—
1100D4—22no—
1101D4—22no—
1102D4—44no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—84no—
1110D4—162no—
1111D4—162no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4#54712yes—
1204C2×C4#57712yes—
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4C2×H(5,𝔽2)11yescharacteristic
1208C2×C4C2×2−1+411yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C8—22no—
1212C8—22no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—42no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—42no—
1233C22—41no—
1234C22—42no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—168no—
1247C22#334814yes—
1248C22C2×#54711yescharacteristic
1249C22#348811yescharacteristic
1250C22#348811yescharacteristic
1251C22C2×#57511yescharacteristic
1252C22C2×#57711yescharacteristic
1253C22C2×#57711yescharacteristic
1254C22#358411yescharacteristic
1255C4—22no—
1256C4—22no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4#349011yescharacteristic
1282C4#351011yescharacteristic
1283C4#353511yescharacteristic
1284C4#353511yescharacteristic
1285C2—24no—
1286C2—81no—
1287C2—82no—
1288C2—161no—
1289C2#4395911yescharacteristic
1290C2C2×#334811yescharacteristic
1291C2#6126311yescharacteristic
1292C2#6197811yescharacteristic
1293C2#6199211yescharacteristic
1294C2#6205511yescharacteristic
1295C2#6206311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59271C2semidirect
3. #32540C2semidirect
4. #32538C2semidirect
5. #32436C2semidirect
6. #32435C2semidirect
7. #32073C2semidirect
8. #32069C2semidirect
9. #30671C2semidirect
10. #30664C2semidirect
11. #28776C2semidirect
12. #27589C2semidirect
13. #27585C2semidirect
14. #27496C2semidirect
15. #27488C2semidirect
16. #26572C2semidirect
17. #26568C2semidirect
18. #25955C2semidirect
19. #25952C2semidirect
20. #25211C2semidirect
21. #25203C2semidirect
22. #24875C2semidirect
24. #24695C2semidirect
25. #24690C2semidirect
27. C2×#2055C2semidirect
28. #22706C2semidirect
29. #22437C2semidirect
30. #22065C2semidirect
31. #21962C2semidirect
33. C2×#485C22semidirect
35. C2×#475C22semidirect
51. #2565C22semidirect
57. #2514C22semidirect
60. #2511C22semidirect
63. #2499C22semidirect
66. #2489C22semidirect
70. #2423C22semidirect
76. #2362C22semidirect
77. #2356C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
93. #2096C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2074C22semidirect
101. #2074C22semidirect
102. #2074C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
110. #2059C22semidirect
111. #2058C22semidirect
122. #2036C22semidirect
123. #2035C22semidirect
127. #2024C22semidirect
130. #1993C22semidirect
131. #1992C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1948C22semidirect
143. #1948C22semidirect
144. #1947C22semidirect
145. #1947C22semidirect
146. #1944C22semidirect
147. #1943C22semidirect
148. #1940C22semidirect
149. #1940C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
162. #1924C22semidirect
163. #1924C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
171. #1873C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
184. #1850C22semidirect
185. #1850C22semidirect
186. #1835C22semidirect
192. #1807C22semidirect
194. #1803C22semidirect
199. C4×#106C22semidirect
201. #1735C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#592712
#592242
#325402
#325382
#324362
#324352
#320732
#320692
#306712
#306642
#287762
#275892
#275852
#274962
#274882
#265722
#265682
#259552
#259522
#252112
#252032
#248752
#248732
#246952
#246902
#242642
C2×#20552
#227062
#224372
#220652
#219622